1. Field of the Invention
This invention relates to a method of measuring ion concentration in a nutrient solution, blood or other various solution, and an ion concentration measuring apparatus for carrying out the method. More specifically, this invention relates to improvements in a method of measuring ion concentration, which is capable of eliminating the interference of ions other than an ion to be measured (hereinafter referred to as a measuring ion), and to an ion concentration measuring apparatus for carrying out the method.
2. Description of the Related Art
Conventionally, a potentiometric ion sensor such as an ion-selective electrode or an ion-sensitive field effect transistor has been employed for measuring the concentration of a measuring ion in a sample solution. These sensors are adapted to measure the concentration of an measuring ion in a sample solution on the basis of the following Nernst equation (1). EQU E=E.degree.+.alpha.log (a) (1)
where E is output potential of the ion sensor in the sample solution, a is the ion activity (concentration) of a measuring ion in the sample solution, .alpha. is the slope (sensitivity) and E.degree. is the output potential (constant) in the standard state. Thus, the equation (1) is inherently formulated for the activity, but the activity can be approximated by the concentration of ion. When a measuring ion is a cation, .alpha. becomes positive value, and when it is an anion, .alpha. or it becomes negative value.
In this case, .alpha. and E.degree. are calculated in advance by using two kinds of standard solutions, each having known ion concentration different from each other. The concentration of a measuring ion can be calculated from the output potential of the ion sensor.
However, an ion sensor may often be influenced to some extent by the interfering ion present in the sample solution. This is because the ion sensor is not exclusively sensitive to the measuring ion, showing some sensitivity to the interfering ion. Therefore, the output of the ion sensor thus obtained is the total of the outputs from the measuring ion and from the interfering ion. Namely, even if the concentration of an measuring ion in a sample solution is constant, the output potential of the ion sensor to be obtained may become altered when the concentration of the interfering ion is varied.
Therefore, when the concentration of an measuring ion is calculated by using the Nernst equation (1), the ion concentration thus calculated may be altered by the influence from the interfering ion even when the concentration of the measuring ion is actually constant, thus setting forth a problem of error in the resultant value. For example, a magnesium ion sensor is susceptible to the interference from calcium ion.
In view of solving the above problem, there has been proposed the Nicholsky-Eiseman equation (2) shown as follows, which is a modification of Nernst equation (1). EQU E=E.degree.+.alpha.log[a.sub.M +.SIGMA.K.sub.MN (a.sub.N).sup.m/n ](2)
where E.degree. and .alpha. are defined in equation (1), a.sub.M is the activity (concentration) of a measuring ion M.sup.m, K.sub.MN is a selectivity coefficient to an interfering ion N.sup.n, a.sub.N is the activity (concentration) of an interfering ion N.sup.n, m and n are the charge numbers of measuring ion and interfering ion respectively, and .SIGMA. represents the sum total of terms of ions which interferes with the measuring ion M.sup.m. The Nicholsky-Eiseman equation is inherently formulated for the activity of ion, but it would not set forth any problem even if the activity of ion is approximated by the concentration of ion.
As for the method of experimentally determining the selectivity coefficient K.sub.MN as defined by the Nicholsky-Eiseman equation, it can be classified into two categories as prescribed in the provision of Japanese Industrial Standard (JIS K O122), i.e. mixed solution method and separate solution method.
In this mixed solution method, the selectivity coefficient is calculated as follows. Namely, the concentration of measuring ion is varied in a solution containing a constant concentration of an interfering ion together with the measuring ion to obtain a curve of the output potential of the ion-selective electrode. Then, the tangent of a region of the curve indicating a change in the output potential in proportion to the change in the measuring ion concentration is determined without being influenced by the interfering ion, and at the same time the tangent of a region of the curve indicating no change of the output potential due to the influence from the interfering ion is determined.
Thereafter, the junction of these tangents is determined, and at the same time the concentration of the measuring ion corresponding to the junction is determined. Finally, the selectivity coefficient is calculated from the relationship between the above concentration of the measuring ion and the concentration of the interfering ion. In contrast to the above, there is a method wherein the concentration of interfering ion is varied in a solution containing a constant concentration of a measuring ion together with the interfering ion.
Meanwhile, in the separate solution method, the response characteristic of the output potential is measured in a measuring ion solution as well as in an interfering ion solution respectively, and the selectivity coefficient is calculated either from the concentrations of these ions indicating the same output potential to each other, or from the output potentials of these solutions indicating the same ion concentrations to each other.
According to these methods, theoretically speaking, the determination of the selectivity coefficient can be made on the basis of three output potentials. However, it is required to make use of additional output potentials other than these three output potentials for determining whether or not these three output potentials are of proper locations in the whole potential response curves. Therefore, in the actual experiment for measuring the selectivity coefficient, at least 5 of 6 kinds of standard solutions are required to be used.
For example, in the case of the mixed solution method, it is required as shown in FIG. 1 to measure two output potentials at the points (G) and (I) in order to determine a potential response curve located on an high ion concentration side and showing an output potential which is proportional to the concentration of an measuring ion. It is also required to measure output potential at the location H for determining whether or not these two points are influenced by an interfering ion.
On the other hand, when a potential response curve which is made constant due to the influence from an interfering ion and located on a low ion concentration side is to be determined, it is required to obtain at least two output potentials (A) and (B) for determining whether or not the potential is saturated. Namely, at least five kinds of solutions each having a different ion concentration from one another are required for accurately measuring the selectivity coefficient by means of the mixed solution method.
Moreover, when it is difficult to predict a specific range for the selectivity coefficient, it is also difficult to predict the range of ion concentration centration which indicates a region of change in output potential, so that many measuring points have to be set at small intervals in a wide range of ion concentration, i.e., at least five kinds of standard solutions differing in ion concentration from one another are required in the actual operation.
On the other hand, in the case of the separate solution method, a total of at least 4 kinds of standard solutions differing in ion concentration from one another, i.e., at least two kinds each for obtaining respective potential response curves for the solution of measuring ion and for the solution of interfering ion. However, even with these methods, there are problems that the response curve measured for an interfering ion solution fails to indicate the same potential slope as that of the response curve measured of measuring ion solution, and that the proportional relationship between the output potential and the concentration of ion on the lower concentration side may be lost, thereby setting forth a possibility that precise selectivity coefficient may not be obtained.
Accordingly, in order to carry out precise measurement by using this conventional method, it is required to prepare at least three kinds of solutions for each ion, i.e., a total of 6 kinds of solutions, and at the same time to perform the comparison of potentials at the same ion concentration, or the comparison of ion concentrations at the same potential in the respective linear region of the potential response curve obtained in advance.
As explained above, when the conventional mixed solution method and separate solution method are to be employed for determining the selectivity coefficient of ion-selective electrode against an interfering ion, at least five kinds of solutions are required, and moreover when it is difficult to predict a specific range for the selectivity coefficient, many more kinds of solutions are required, thereby making the measuring operation as well as the calculation involved therefor rather troublesome and complicated.